Writing and Solving Equations

Big Idea:
Paul Pierce made 14 more points than Kevin Garnett. Let k represent Kevin Garnett’s points. Write an expression to show how many points Pierce made. If Pierce made 26 points, how many points did Garnett make? Students work on writing and solving equat

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day. Today I want students to review writing expressions and creating and solving equations from the previous lessons.

Problem one can be difficult for some students. If students struggle to write an expression, I ask them what they know and what they are trying to model. I want students to understand that twice the amount of Elizabeth’s crayons would be 2e, and three more than that would be 2e + 3 or 3+2e.

For problem 2 and 3 I ask a student to share and explain their thinking. I call on other students to share if they agree and disagree and why. Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

Resources (3)

Resources

I ask students, “What is the difference between an algebraic expression and an algebraic equation?” I want students to recognize that an expression shows the relationship between a variable and numbers. An algebraic equation sets two expressions equal to each other, like the balance we used in the previous lesson. Solving an equation is the process of figuring which values make the equation true. I also review that if a variable is right next to a number, the two are being multiplied together. I remind students they can also use the dot to show multiplication, but that we should avoid using the x symbol because it can be confused as a variable.

I tell students that they must read through the scenarios and decide whether equation a or b fits that scenario. Students participate in a Think Write Pair Share. I call on students to share out their thinking. I ask students, “How do you know that equation works? Why can’t the other equation work?” Even though both scenarios include the same values, I want them to recognize the difference between equation a and b.

Then I ask students to work with their partner to figure out the value of x for equation a and b. What value must x be in order to make the equation true? Students are engaging with MP2: Reason abstractly and quantitatively. Some students may guess a value and check the answer and then readjust as needed. Other students may use the inverse operation to figure out the value of x. I ask two students who used these two strategies to show and explain their work. I do not explicitly teach students to use the inverse operations step by step. In the past when I have taught this way, students have memorized the procedure oftentimes without having a deep understanding of what they were doing and why it worked.

I Post A Keyso that groups can get up and check their work as they finish each page. I have groups check in with me when they finish a page, so I can make sure they are on track.

We work on Part A together. I have a volunteer read the situation out loud. I ask, “What is going on?”, “What do we know?” and “What does the variable represent?”. If students struggle to see that the expression would be 2w, I substitute 11 in for w. What if the plant grew for 11 weeks, how tall would it be? Sometimes it’s easier for students to replace the variable with a number to understand what operation they would use. I ask students how to set up the equation and how to solve for w. I require students to use substitution to prove that their value for x works. I ask students, “Are there any other values that would also work for x?”. I want students to realize that for this particular equation, x can only be 8.

Students move into their groups. As students work, I walk around and monitor student progress. Students are engaging in MP2: Reason abstractly and quantitatively and MP4: Model with mathematics.

If students are struggling, I may ask them the following questions:

What is going on in the situation?

What do you know?

What does the variable stand for?

What operation is going on between the value and the variable? How do you know?

What is the difference between an expression and an equation?

How can you prove that your value for x works?

Are there any other values for x that would also work? Why or why not?

If students are correctly working through the examples, they can move onto the challenge questions.

I ask students to turn to Part G. I ask students to share their thinking about the expression, equation, and the number of points Kevin Garnett made. I ask other students to share if they agree or disagree with the other students’ thinking and why. I want students to understand that if Paul Pierce made 26 points, then Kevin Garnett must have made 12 points since 12 + 14 = 26. As a challenge question I ask, “Garnett and Pierce made a total of 50 points. How many points did each player make?” Students participate in a Think Pair Share. I want students to be able to extend the pattern and see that Pierce still has to make 14 more points than Garnett. Some students may guess and check, while others may work backwards. If students are still working on it, I tell them they can continue thinking about it after they complete their ticket to go.

This is the first lesson that I have used from this site. I was looking for something to supplement what we had already done with expressions. This real world application helped most of my 6th graders get the idea that expressions are really useful.